Since I don't intend to make this simply a blog for sports reporting, I offer a new topic, dedicated to Brian. It is heavy on probability, so if you don't want to think, stop reading.
Here is my take on the so-called Monty Hall Paradox. The problem goes like this:
You are on the classic show "Let's Make a Deal", with the infamous Mr. Hall. You have three doors from which to choose, with only one door being a winner. After you make your choice, Monty reveals one of the other doors as a loser, and offers you the opportunity to switch to the third, unopened door. Do you switch, and why? The paradox comes in because your chances of picking the winner go up by switching. At first, I didn't believe it, but in practice it is true. It seems initially that there are 8 possibilities, set out like this:
Three doors, A, B, C, with A being the winner.
Choice #1 you pick A, they reveal B, you stay with A = win
Choice #2 you pick A, they reveal C, you stay with A = win
Choice #3 you pick A, they reveal B, you change to C = loss
Choice #4 you pick A, they reveal C, you change to B = loss
Choice #5 you pick B, they reveal C, you stay with B = loss
Choice #6 you pick B, they reveal C, you change to A = win
Choice #7 you pick C, they reveal B, you stay with C = loss
Choice #8 you pick C, they reveal B, you change to A = win
Half of the time when you switch, you lose. The trouble with that view is that choices 1 & 2 are no different. Your choices really are:
Choice #1 you pick A, they reveal a loser, you stay = win
Choice #2 you pick A, they reveal a loser, you switch = loss
Choice #3 you pick a loser, they reveal a loser, you switch = win
Choice #4 you pick a loser, they reveal a loser, you stay = loss
That still seems like it's a 50-50 deal, but it's not. You have only three choices. You improve your chances of winning by ensuring what is left for you to switch to.
Choice #1 you pick A, they reveal a loser, you switch = loss
Choices #2 & #3 you pick a loser, they reveal a loser, you switch = win
Your choices boil down to sticking with your first pick (33%), or switching to the other door (67%). Your chances of winning double by switching. Strange, but true.